org.netlib.lapack
Class SLAED3

java.lang.Object
org.netlib.lapack.SLAED3

public class SLAED3

extends java.lang.Object

SLAED3 is a simplified interface to the JLAPACK routine slaed3.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.

* ..
*
* Purpose
* =======
*
* SLAED3 finds the roots of the secular equation, as defined by the
* values in D, W, and RHO, between 1 and K. It makes the
* appropriate calls to SLAED4 and then updates the eigenvectors by
* multiplying the matrix of eigenvectors of the pair of eigensystems
* being combined by the matrix of eigenvectors of the K-by-K system
* which is solved here.
*
* This code makes very mild assumptions about floating point
* arithmetic. It will work on machines with a guard digit in
* add/subtract, or on those binary machines without guard digits
* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
* It could conceivably fail on hexadecimal or decimal machines
* without guard digits, but we know of none.
*
* Arguments
* =========
*
* K (input) INTEGER
* The number of terms in the rational function to be solved by
* SLAED4. K >= 0.
*
* N (input) INTEGER
* The number of rows and columns in the Q matrix.
* N >= K (deflation may result in N>K).
*
* N1 (input) INTEGER
* The location of the last eigenvalue in the leading submatrix.
* min(1,N) <= N1 <= N/2.
*
* D (output) REAL array, dimension (N)
* D(I) contains the updated eigenvalues for
* 1 <= I <= K.
*
* Q (output) REAL array, dimension (LDQ,N)
* Initially the first K columns are used as workspace.
* On output the columns 1 to K contain
* the updated eigenvectors.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N).
*
* RHO (input) REAL
* The value of the parameter in the rank one update equation.
* RHO >= 0 required.
*
* DLAMDA (input/output) REAL array, dimension (K)
* The first K elements of this array contain the old roots
* of the deflated updating problem. These are the poles
* of the secular equation. May be changed on output by
* having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
* Cray-2, or Cray C-90, as described above.
*
* Q2 (input) REAL array, dimension (LDQ2, N)
* The first K columns of this matrix contain the non-deflated
* eigenvectors for the split problem.
*
* INDX (input) INTEGER array, dimension (N)
* The permutation used to arrange the columns of the deflated
* Q matrix into three groups (see SLAED2).
* The rows of the eigenvectors found by SLAED4 must be likewise
* permuted before the matrix multiply can take place.
*
* CTOT (input) INTEGER array, dimension (4)
* A count of the total number of the various types of columns
* in Q, as described in INDX. The fourth column type is any
* column which has been deflated.
*
* W (input/output) REAL array, dimension (K)
* The first K elements of this array contain the components
* of the deflation-adjusted updating vector. Destroyed on
* output.
*
* S (workspace) REAL array, dimension (N1 + 1)*K
* Will contain the eigenvectors of the repaired matrix which
* will be multiplied by the previously accumulated eigenvectors
* to update the system.
*
* LDS (input) INTEGER
* The leading dimension of S. LDS >= max(1,K).
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: if INFO = 1, an eigenvalue did not converge
*
* Further Details
* ===============
*
* Based on contributions by
* Jeff Rutter, Computer Science Division, University of California
* at Berkeley, USA
* Modified by Francoise Tisseur, University of Tennessee.
*
* =====================================================================
*
* .. Parameters ..